PULSED NEUTRON SOURCE MEASUREMENTS OF KINETIC PARAMETERS IN THE SOURCE-DRIVEN FAST SUBCRITICAL

CORE MASURCA

E. GONZÁLEZ-ROMERO, D. VILLAMARÍN, M. EMBID CIEMAT

enrique.gonzalez@ciemat.es

G. ALIBERTI, G. IMEL, V. KULIK, G. PALMIOTTI ANL

C. DESTOUCHES, F. MELLIER, C. JAMMES, G. PERRET

CEA Cadarache DEN/DER/SPEx/LPE

A. BILLEBAUD, R. BRISSOT, D. HEUER, C. LE BRUN, E. LIATARD, JM.LOISEAUX, O. MÉPLAN, E. MERLE, F. PERDU, J. VOLLAIRE.

Laboratoire de Physique Subatomique et de Cosmologie CNRS-IN2P3/UJF

A. D'ANGELO, M. CARTA, V. PELUSO ENEA

J.L. KLOOSTERMAN, Y. RUGAMA

IRI, Delft University of Technology

P. BAETEN SCK-CEN

F. GABRIELLI

Turin Polytechnic Institute

In the framework of the European 5FP MUSE(*) project, measurements are being performed to investigate the neutronic behavior of the fast subcritical core MASURCA coupled with the GENEPI accelerator. The most direct method to study the response of the system to source intensity variations, is to inject a short neutron pulse and record the counting rate following the pulse of detectors distributed on different reactor positions. With the help of GENEPI neutron pulses, less than 1µs wide, have been generated in the center of MASURCA with frequencies of 0.5 to 4 kHz, and the subsequent neutron flux has been observed by detectors based on 235U and 237Np fission placed in the core, reflector and shielding regions of MASURCA. Different core configurations, corresponding to different levels of subcriticality, have been explored. The results of these measurements are presented in this paper. Several analyses have been performed to extract information of the reactivity of the MASURCA configurations from the analysis of the prompt nearly exponential decay, measuring either the reactor α value, reactivity in dollars, or the prompt neutron multiplication.

(*) This work has been partially supported by the 5FP EU Contract – n° FIKW-CT-2000-00063

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1. Introduction

The main objective of the MUSE project performed in the framework of the European 5FP, is to improve the understanding of the kinetic response of Accelerator Driven Subcritical systems, ADS, and to develop methodologies for their reactivity determination and monitoring that do not require to refer to criticality, using this kinetic response.

The most direct method to study this kinetic response of a system is to inject an instantaneous neutron pulse. In MUSE, the GENEPI accelerator has been used to produce very short pulses (<1µs long) by the deuterium-deuterium, DD, or deuterium-tritium, DT, reactions in the center of the MASURCA core. The signals from 235U and 237Np fission detectors placed in the core, reflector and shielding have been independently recorded and analyzed by up to 5 different data acquisition systems and experimental teams. Different configurations of the MASURCA core ranging from close to critical (ρ≅ 1.5$ keff ≅ 0.995), to subcritical (ρ≅ 9$ keff ≅ 0.97), and to deep subcritical (ρ≅ 44$ keff ≅ 0.87) had been explored.

The global MUSE program, GENEPI and MASURCA, are described in another contribution to this workshop [1] and elsewhere [7]. In this paper we summarize the performed pulsed neutron source experiments, PNS, and the preliminary results obtained in the SC0 and SC2 periods.

2. Pulsed neutron source experiments

2.1. Experimental results

In the PNS experiments, neutron pulses of 3×104 n/pulse for DD or 3×106 n/pulse for DT, are injected at the center of the MASURCA subcritical core, with a repetition rate ranging from 0.5 to 4.5 kHz. The delay of the signals from the different detectors respect to the closest preceding neutron pulse, reduced detection times, are recorded and analyzed to produce histograms describing the kinetic response of MASURCA. Figure 1 presents a typical result of these histograms for three 235U detectors located in the core.

The configurations used for PNS measurements are identified by the core configuration and the safety (SR) and pilot rod (PR) positions. The configurations used were: SC0 with 1086 fuel cells and SC0 with 1108 fuel cells, that when unperturbed have reactivities close to ρ≅ 1.5$ keff ≅ 0.995, and the SC2, that has a reactivity close to ρ≅ 9$ keff ≅ 0.97 when unperturbed. In both cases, data has been collected with the PR in two positions, up and down, with a difference of reactivity close to 0.4$, and with one safety rod inserted, reducing the reactivity in 3000 to 4500 pcms.

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The histograms of reduced times of core detectors show three main features for unperturbed SC0 configurations . There is a non negligible constant base level before and long after (>400 µs) the arrival of the GENEPI pulse, a prompt increase with a very narrow (≈1µs) peak after the pulse followed by a nearly exponential decay to the base level. The base level is produced by the combination of intrinsic source and GENEPI induced fissions delayed neutrons.

Figure 1. Typical reduced time histogram of signals from fission monitors in the core, collected in the SC0 configuration with DT and illustration two PNS analysis methods.

The shape of the histogram changes for different detector positions and reactivities. Figure 2 shows the reduced times histogram for the detectors located in the core (a), the reflector (b) and the shielding (c) for the SC0 configuration with the 4SR up and the PR down [7]. In these histograms, the constant base level has been subtracted allowing to appreciate more clearly the exponential decay at longer times. The shape of the histograms in the reflector shows a much smoother increase in the counting rate and a rounded maximum, ≈14 µs after the GENEPI pulse, followed by a nearly exponential decay, but with a logarithmic derivative slowly decreasing as time increases. The logarithmic derivative only reaches the same value as in the core detectors at times as long as 200 µs after the GENEPI pulse. A similar behavior is observed in the monitors located in the shielding, with even slower approach to the maximum, found ≈18 µs after the GENEPI pulse. On the other hand the signals from detectors in a given region (detectors in symmetrical positions) show very similar shape.

Monte Carlo simulations allow to explain this behavior of the histograms from the reflector and shielding monitors as a combination of the progressive moderation of the neutron spectra in these regions, and the high sensitivity of the 235U fission based monitors to the slower neutrons. As a consequence, a 237Np fission detector, sensitive to neutrons of energies above 0.5 MeV, was placed

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inside the reflector. Figure 2(d) shows the comparison (after arbitrary normalization) of the reduced time histograms for this detector and for 235U monitors in the core, the reflector and the shielding.

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- 235U Detector A (Shield)- 235U Detector I (Core)- 235U Detector N (Reflector)- 237Np (Reflector)

(d) 235U in different regions and 237Np in

the reflector Figure 2. Shapes of the reduced time histograms for detectors placed in different positions in the SC0 configuration with 4SR up and the PR down, using the tritium target. The constant base level has been subtracted from each histogram.

The shape and time scale of the reduced time histogram also depend on the subcritical system reactivity. This dependence was explored by PNS measurements of SC0 configurations modified by introduction of one or the four safety rods and in the SC2 configurations. Figure 3(a) shows the reduced time histograms for SC0 with 3SR up the SR1 down and the PR down, resulting in Keff close to 0.96. Figure 3(b) shows the corresponding histograms for SC0 with the 4SR inserted, resulting in Keff close to 0.86, and Figure 3(c) displays the corresponding histograms for SC2 unperturbed configuration with Keff close to 0.97. In all cases, the figures present the data for monitors in the three different regions of MASURCA, using the DT source. The most relevant feature is the change on the exponential decay rate, very sensitive to the subcritical system reactivity that is the basis of the application of this measurement to the determination of the reactivity of subcritical systems. Figure 3(d) illustrates this sensitivity comparing the reduced time histograms of one in-core monitor (F)

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and the 237Np reflector detector for the SC0 and SC2 configurations with the PR up versus down.

__ Detector N (Reflector)

N

A

(a) SC0 with 3SR↑ SR1↓ PR↓

Detector N (Reflector)

SC0- DT- 4SR down

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SC2- Clean Configuration

- 235U Detector I (Core)- 235U Detector N (Reflector)- 237Np (Reflector)

I

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__ 237Np Reflector SC0 PR down

--

--

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(d) SC0 and SC2 ⊗ PR↓ vs. PR↑

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Figure 3. Shapes of the reduced time histograms for modified SC0 configurations resulting in lower reactivities and unperturbed SC2 configuration. The constant base level has been subtracted from each histogram.

2.2. Analysis methods

The PNS histograms had been analyzed to extract the kinetic parameters of the subcritical assembly by three conceptually different methods.

In the first analysis method, known as the area method [2], the ratio of prompt and delayed fission detections is used to compute the ratio ρ/β or the reactivity in dollars, ρ$, by the equation ρ/β=prompt/delayed. In order to evaluate the delayed fission detections, the intrinsic source contribution to the constant base level (Figure 1) has to be subtracted. This can be done using a previous calibration run without GENEPI source, or combining the data of two runs performed with different GENEPI frequencies. In this paper we will present only the results using calibration runs. After subtraction, the delayed counting rate can be computed by fitting the constant base level, in particular at the end of the period between GENEPI pulses, and multiplying by the period of the GENEPI source. A small correction (< 3% in all cases) has been applied to take

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into account the measured fluctuations of the GENEPI time interval between consecutive pulses within each measurement. The prompt contribution to the fission detections is obtained by subtraction of the delayed contribution from the total counting per pulse. Table 1 shows the ρ$ values for SC0 in the two unperturbed configurations with the DT source for frequencies of 0.5 and 1 kHz. Table 2 displays the ρ$ results for SC0 configurations with one SR inserted with the DT source with 1 kHz frequency. Finally Table 3 presents its values for the two SC2 unperturbed configurations.

Table 1. PNS area method determination of ρ$ for SC0 unperturbed configurations with the DT source at 0.5 and 1 kHz.

F 1.58 ±0,01 1.98 ±0,01 0.40 ±0,01 1.58 ±0,01 1.99 ±0,01 0.41 ±0,01I 1.60 ±0,01 2.00 ±0,01 0.40 ±0,01 1.59 ±0,01 2.00 ±0,01 0.41 ±0,01L 1.60 ±0,01 2.00 ±0,01 0.40 ±0,01 1.59 ±0,01 2.01 ±0,01 0.42 ±0,01M 1.60 ±0,01 2.00 ±0,01 0.40 ±0,01 1.60 ±0,01 2.00 ±0,01 0.40 ±0,01N 1.58 ±0,01 1.99 ±0,01 0.41 ±0,01 1.60 ±0,01 1.99 ±0,01 0.39 ±0,01G 1.60 ±0,01 2.02 ±0,01 0.42 ±0,01 1.60 ±0,01 2.03 ±0,01 0.43 ±0,01H 1.58 ±0,01 2.00 ±0,01 0.42 ±0,01 1.60 ±0,01 2.01 ±0,01 0.41 ±0,01A 1.60 ±0,01 2.01 ±0,01 0.41 ±0,01 1.60 ±0,01 2.02 ±0,01 0.42 ±0,01B 1.61 ±0,01 2.01 ±0,01 0.40 ±0,01 1.60 ±0,01 2.03 ±0,01 0.43 ±0,01

Mean RMS Mean RMS Mean RMS Mean RMS Mean RMS Mean RMS1.59 0.01 2.00 0.01 0.41 0.01 1.60 0.01 2.01 0.02 0.41 0.01

Reflector

Shielding

Global

Detector PR Up 1kHz ρ($) PR Down 1kHz ρ($) ∆ρ ($) 1kHz PR Up 0.5kHz ρ($) PR Dw 0.5kHz ρ($) ∆ρ ($) 0.5 kHz

Fuel

Table 2. PNS area method determination of ρ$ for SC0 configurations with one SR inserted (DT source at 1kHz). *Note that detector ‘I’ is very close to SR1 and has been excluded from statistics.

F 11,9 ±0,1 13,6 ±0,1 1,7 ±0,1I* 14,3 ±0,1 14,1 ±0,1 -0,2 ±0,1L 12,9 ±0,1 14,4 ±0,1 1,5 ±0,1M 12,7 ±0,1 13,9 ±0,1 1,2 ±0,1N 12,1 ±0,1 13,9 ±0,1 1,8 ±0,1G 13,0 ±0,1 14,5 ±0,1 1,5 ±0,1H 12,6 ±0,1 14,2 ±0,1 1,6 ±0,1A 12,7 ±0,1 14,1 ±0,1 1,4 ±0,1B 13,0 ±0,1 14,1 ±0,1 1,1 ±0,1

Mean RMS Mean RMS Mean RMS12,6 0,4 14,1 0,3 1,48 0,24

Detector 3SR up SR1 down ρ($) 3SR up SR2 down ρ($) ∆ρ ($)

Fuel

Reflector

Shielding

Global

Table 3. PNS area method determination of ρ$ for SC2 unperturbed configurations.

F 8.55 ±0,15 9.05 ±0,14 0.50 ±0,21I 8.85 ±0,15 9.25 ±0,14 0.40 ±0,21L 8.94 ±0,15 9.41 ±0,14 0.47 ±0,21M 8.67 ±0,15 9.12 ±0,14 0.45 ±0,21N 8.90 ±0,15 9.34 ±0,14 0.44 ±0,21G 9.06 ±0,15 9.54 ±0,14 0.48 ±0,21H 8.92 ±0,15 9.38 ±0,14 0.46 ±0,21A 8.87 ±0,15 9.41 ±0,14 0.54 ±0,21B 8.97 ±0,15 9.37 ±0,14 0.40 ±0,21

Mean RMS Mean RMS Mean RMS8.86 0.16 9.32 0.15 0.46 0.04

Fuel

Reflector

Shielding

Global

Detector ρ PR Up ($) ρ PR Down ($) ∆ρ ($)

The results of tables 1 and 4, for two different configurations and data acquisition systems, show their independency on the GENEPI frequency.

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Table 4. PNS area method determination of ρ$ for SC0 configurations with SR1 inserted at different GENEPI frequencies with a different DAQ as Tables 1 and 3.

Frequency (kHz) Detector ρ ($) Average St dev 0,5 F - 12,2 - 12.13 0.2 % 1 F - 12.1 2 F - 12.1

0.5 I - 14.3 - 13.87 1 % 1 I - 13,7 2 I - 13,6

0.5 L - 13.2 - 13.23 0.2 % 1 L - 13,2 2 L - 13,3

The second method consists, for unperturbed SC0, on a non-linear fit of the exponential approaching to the constant base level by the sum of a constant and an exponential (Figure 1). According to point kinetics [3], the constant of the exponential decay is α=(β−ρ)/Λ. Point kinetics requires that, the spatial and energy distributions of the neutrons in the subcritical system, or at least in the detector position, have achieved its asymptotic behavior. This takes place at different reduced times in different regions and in particular in the reflector and the shielding. There the low absorption macroscopic cross section, allow a continuous moderation process of the neutron spectra for periods as long as 150µs. As a consequence, the fit is applied to the data in a selected interval and the variation with the interval limits is quoted as systematic uncertainty. In most cases the statistical uncertainty is, at least, 4 times smaller than the systematic. Table 5 presents the α values obtained for the unperturbed 1108 cells SC0 configurations, showing a progressive decrease going from the core to the reflector and to the shielding, as expected from Figure 2. The values from the core detectors or the 237Np reflector detector should be used to characterize the system.

Table 5. PNS determination of α by fitting to one exponential for the 1108 cells SC0. In the conversion between α and ρ it has been assumed that β=335 pcm and β/Λ= 5800 s-1.

F 14360 ±50 16700 ±50 2340 ±70 0.40 ±0.01I 14350 ±50 16700 ±50 2350 ±70 0.41 ±0.01L 14360 ±50 16700 ±50 2340 ±70 0.40 ±0.01M 13960 ±120 16020 ±130 2060 ±180 0.36 ±0.03N 13910 ±110 16000 ±130 2090 ±170 0.36 ±0.03G 14050 ±100 16110 ±100 2060 ±140 0.36 ±0.02H 14020 ±100 16060 ±80 2040 ±130 0.35 ±0.02

237Np 16780 ±80 A 13650 ±100 15630 ±130 1980 ±160 0.34 ±0.03B 13630 ±100 15600 ±140 1970 ±170 0.34 ±0.03

Detector

Fuel

Reflector

Shielding

α PR Up (s-1) α PR Down (s-1) ∆α (s-1) ∆ρ ($)

Table 6 shows the independency of the fitted α value with the GENEPI frequency in the range from 1 to 4 kHz, using different data acquisition and analysis team in the 1086 cells SC0 configuration.

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Table 6. α versus GENEPI frequency in the 1086 cells SC0 configuration with PR up and with a different DAQ than in Table 5.

Freq. (kHz) α (s –1) and σα/δ (%) Core Monitors Reflector Monitors F I A C 1 12849 1.6/2.8 12645 1.4/3.7 12397 0.6/1.1 12336 0.6/1.0 2 13123 1.3/1.3 13014 1.0/2.6 12217 0.7/1.4 12314 0.7/1.7 3 13193 1.4/3.4 13484 1.1/2.0 12239 0.7/1.1 12225 0.7/1.5 4 13348 1.5/1.7 13213 1.2/3.0 12123 0.9/1.7 12292 0.8/1.2

ασα 13128 1.6% 13089 2.7% 12244 0.9% 12292 0.4%

When trying to apply the same procedure to more subcritical configurations, SC2 or SC0 with one SR down, reasonable fits can not be achieved with a single exponential approach. As Figure 3 (a-c) shows, the counting rate outside the core decays at long times following a characteristic time constant, with no or small dependence on reactivity and slower than the slope at shorter times. Monte Carlo simulations show that this effect is due to slow neutrons (few eV and slower) that can survive in the reflector and shielding longer than the fission chain is sustained in the core. The effect is much smaller for detectors in the core or fast reflector detectors, but not completely negligible, indicating a small coupling between the core and those slow neutrons in the reflector. When this coupling is introduced in the kinetic equations of a 2 regions 2 energy groups model, the predicted counting rate evolutions can be described by the sum of 2 exponentials [4]. Table 7 shows the α values obtained by a nonlinear two exponential fit. The quoted systematic uncertainties are dominated by the choice of the fitting interval and the correlation between the two exponential constants in the fits. Reasonable agreement is found between core and reflector detectors, but there is a tendency to find lower α values in the core. Further work is in progress to analyze this effect and improve precision by reducing the correlations in the fits.

Table 7. PNS determination of α by fitting two exponentials for SC2 configurations. In the conversion between α and ρ it has been assumed that β=335 pcm and β/Λ= 5800 s-1.

F 53000 ±1200 56300 ±1200 3300 ±1700 0.6 ±0,3I 55200 ±1300 55700 ±1300 500 ±1800 0.1 ±0,3L 57600 ±1600 58500 ±1600 900 ±2300 0.2 ±0,4M 54800 ±500 58000 ±500 3200 ±700 0.6 ±0,1N 57900 ±600 59000 ±600 1100 ±800 0.2 ±0,1G 62200 ±600 64800 ±600 2600 ±800 0.4 ±0,1H 64700 ±600 67100 ±600 2400 ±800 0.4 ±0,1

237Np 53100 A 55000 ±3000 68000 ±3000 13000 ±4000 2.2 ±0,7B 66000 ±3200 76000 ±3200 10000 ±5000 1.7 ±0.7

Detector α PR Up (s-1) α PR Down (s-1) ∆α (s-1) ∆ρ ($)

Fuel

Reflector

Shielding

The third analysis approach is based on the distribution of time P(τ) between two fissions, taking into account the effect of neutrons coming back from the reflector [5]. This P(τ) distribution is obtained by a MCNP calculation and once normalized it appears to be independent on small change of the fuel or

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reflector size. Using the normalized distribution P’(τ) it is possible to calculate the neutron population N(t,kp) by summing the contribution of each generation present in the reactor. N(t,kp) is then written as :

N (t,kp) = kp P'(τ) + kp 2 P'(τ)*P'(τ) + kp

3 P'(τ)*P'(τ)*P'(τ) + ...

where the star denotes the convolution operator. The logarithmic derivative α(t,kp) of the neutron population, which is equal to :

dt

ktdN

ktNkt p

pp

),(

),(1

),( =α

is compared to the experimental one. Finally the value of the kp parameter leading to the α(t,kp) function fitting the best the experimental decrease rate gives the prompt multiplication factor.

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Figure 4. kp and keff values for the SC0, left, and SC2, right, configurations obtained with

the Monte Carlo based analysis method.

This method has been applied to measurements performed in three core configurations (SC0 PR up and down and SC2 PR down). A 235U fission chamber was used in the three cases. Figure 4 shows the experimental exponential decrease rate and the α(t,kp) function that fits best the experimental results.

Table 8. kp and keff values for the SC0 and SC2 configurations obtained with the MC based analysis method.

Configuration Detector kp keff SC0 PR up 235U 0.9913±0.0005 0.9946±0.0005

SC0 PR down 235U 0.9892±0.001 0.9925±0.001 SC2 PR down 235U 0.9674±0.002 0.9706±0.002

An excellent agreement is found between the calculated and experimental slopes on a time scale ranging from 5 µs up to 100 µs after the neutron pulse. The value of kp obtained for the three configurations are summarized in table 8, together with the estimated keff using βeff=335 pcm.

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Table 9. Comparison of different PNS analysis methods and with rod drop [6,7] results.

MUSE configurationSC0 (1108) 4SR ↑ PR ↑ 1.59 ± 0.01 1.48 ± 0.01 1.62 ± 0.15 1.50 ± 0.10SC0 (1108) 4SR ↑ PR ↓ 2.00 ± 0.01 1.88 ± 0.01 2.26 ± 0.3 1.92 ± 0.11SC0 (1108) 4SR ↑ PR ↓−↑ 0.41 ± 0.01 0.40 ± 0.01 0.64 ± 0.34 0.42 ± 0.15SC0 (1108) 3SR ↑ SR1 ↓ PR ↓ 12.6 ± 0.1 11.7 ± 0.2SC0 (1108) 3SR ↑ SR2 ↓ PR ↓ 14.1 ± 0.1 13.5 ± 0.4SC0 (1108) 3SR ↑ SR2-SR1 ↓ 1.48 ± 0.14 1.8 ± 0.4SC2 4SR ↑ PR ↑ 8.86 ± 0.15 9.2 ± 0.3SC2 4SR ↑ PR ↓ 9.32 ± 0.14 9.7 ± 0.4 9.0 ± 0.6SC2 4SR ↑ PR ↓-↑ 0.46 ± 0.21 0.5 ± 0.5

PNS ρ($) area ratio PNS ρ($) α fit PNS ρ($) kp fr MC Rod Drop

Table 9 presents a comparison of the results from the different PNS analysis methods and with the rod drop reactivity values. In the conversion between α and ρ the same β and Λ values been assumed for all configurations, although Monte Carlo simulations indicate a small increase on Λ from SC0 to SC2. All values agree with the rod drop results within the respective uncertainties. The very high precision of the area method and the α slope fit, allows to appreciate the possibility of small systematic differences (30pcm) between the absolute values of those reactivity estimators, that disappear in the differences of small relative reactivity changes.

3. Comparisons of ADS simulation tools and PNS experiments

One of the main goals of the MUSE project is to validate ADS simulation tools. In this sense, a large effort is conducted inside a NEA/OCDE calculation benchmark to simulate the main MUSE experiments, including PNS. In total 16 participants are contributing with 34 solutions. In addition, special efforts are being applied to develop new tools and check the ultimate limits of our simulation programs. Figure 5, shows the comparisons of the deterministic simulation of the reduced times histograms for a core (F) and a reflector (C) detectors in SC0 with 3SR up and SR1 and PR down with the DD source, using the new ERANOS module, KIN3D.

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Figure 5. Deterministic (KIN3D/ERANOS) simulations versus experimental data.

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Figure 6, presents the comparison of high statistics Monte Carlo simulations, MCNP4c3 with JEF2.2 and JEFF3.0 (239Pu & Fe) libraries, of DT pulses in SC2 with 4SR up PR down, with the experimental data of a core (F) and a reflector (N) detectors. Both simulations show good agreement for the core detectors (in the MC case data and simulation are hard to distinguish), but some discrepancies at long times in the reflector. These difficulties are related with the transport of very slow neutrons that dominate the counting rate in 235U fission detectors in the reflector, showing that further work is required in this topic.

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Figure 6. Monte Carlo simulations (MCNP4c3) versus experimental data.

4. Applications to industrial ADS and conclusions

In industrial ADS, accelerator and core limitations will make difficult to prepare and use pulses as short as provided by GENEPI, however very fast proton beam (neutron source) shut-down will be possible. The detector signals in this situation can be calculated from the MUSE experimental data, by convolution of the reduced time histograms and the accelerator current time dependence. This has been done for a SC2 configuration for core and reflector detectors. Figure 7 shows the result of this convolution for the F (core) detector.

Prompt contribution

Delayed contribution

ρ$ = PromptDelayed

Beam interruption

Asymptotic level within 0.1% @ 150µs

Detector in the core in SC2

Figure 7. Extrapolation of a MUSE experimental pulse to ADS fast beam interruption.

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The area method can be directly translated to this experiment, as shown on the Figure 7, and ρ$ can be computed from the counting rate before the interruption and the asymptotic value just after. This asymptotic value is reached with 0.1% precision 150 µs after the interruption for core and 237Np reflector detectors and 250 µs after the interruption by the 235U reflector detectors.

After subtraction of the asymptotic level the counting rate of core detectors and 237Np reflector detectors presents a simple decay that can be described by two exponentials that will still allow to obtain the α constant. The 235U reflector detector have a more complicated response and more work is needed to develop the PNS slope methodology if α should be obtained from these detectors.

The Monte Carlo based methods also have the potentiality to allow obtaining the prompt neutron multiplication constant, kp, but work is still needed to adapt this methods to experiments with an interruption of a continuous beam.

It should be noted that Λ can be different in MUSE and in the industrial ADS, making necessary a normalization in all the times quoted in this section.

In summary, in this paper we have shown that PNS measurements are very useful tool to characterize subcritical systems and to evaluate its reactivity, with high sensitivity, reproducibility and low uncertainties. Different analysis methods, that can be extrapolated to industrial scale ADS, had been applied showing very promising results, although a final comparison with other evaluations of the reactivity, still in progress, is needed to evaluate the possible biases and systematic uncertainties of each method.

References

1. F. Mellier et al. Progress of the MUSE-4 experiments and first results from the measurements at subcriticality levels representative of an ADS. Proceedings of this workshop.

2. N. G. Sjöstrand. Measurements on a subcritical reactor using a pulsed neutron source. Arkiv Fysik, 11, 233 (1956).

3. R. E. Uhrig. Random Noise Techniques in Nuclear Reactor Systems. Ronald Press, N. Y., 1970.

4. D. Villamarin. Dynamical analysis of the MUSE-4 experimental subcritical nuclear assembly coupled with a pulsed external neutron source. PhD Thesis in preparation, Univ. Complutense, Madrid (2003).

5. F. Perdu, et al., Prompt reactivity determination in a subcritical assembly through the response to a dirac pulse, Prog. Nucl. Energy, 42, 107 (2003).

6. G. Perret. Développement et amélioration des méthodes de détermination de la réactivité - maîtrise des incertitudes associées. PhD Thesis in preparation, CEA, Cadarache (2003).

7. MUSE Collaboration. Experiment Report – Reference and SC0 Configurations. Report to EC, 2003.